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Hydrodynamic models

Calibration, validation and data assimilation for hydrodynamic models of tide propagation along the coast and on the continental shelf require quality tide measurements to define the boundary conditions of the models. For open boundary conditions at sea, there is the problem of obtaining sea level measurements in areas several hundred metres deep.

How hydrodynamic modelling works

Numerical modelling consists of solving the hydrodynamic equations directly in the tidal wave propagation zone. In theory, it is used to calculate the tide at any point in the zone.

It involves dividing the zone into elements of simple geometry, called grid cells, and applying the following principles:

the principle of conservation, wherein the variation of water level in a grid cell results from the difference between the amount of water entering the cell and the amount of water exiting from the sides. This difference depends exclusively on the current running through the grid;

the principle of dynamics, wherein the variation of flow velocity in a grid cell depends on external forces acting on the column of water contained in the cell. There are three types of forces:

pressure forces due to differences in water level in the surrounding grid cells;

Coriolis force due to the rotation of the Earth which in the northern hemisphere, tends to bend the direction of the current to the right;

braking force similar to friction, which is exerted near the bottom and sides of the grid cells.

The variations in water levels and velocity in a grid cell depends on water levels and currents in the neighbouring grid cells. All grid cells are interdependent and the problem of the variation of water levels and currents must be resolved globally throughout the area studied.

The tide: the driving force behind hydrographic movements

Movements can only exist if there is a driving force. Here this driving force is constituted by the tide at the open boundaries of the model, which are not composed of a coastline. This forced movement propagates from cell to cell across the entire zone.

Effect of bathymetric data

The calculations are performed at regular "time step" intervals from a situation at rest. The results are usable only after a stabilization period corresponding in practice to two or three tidal cycles.

In practice, the grid cells are squares, rectangles or triangles (finite elements). The choice of the cell size is key: the smaller they are, the better the accuracy. However, the smaller the cells, the more cells there are for a given area.

Moreover, the time step is not independent of the grid cell size: too large a time step can generate numerical instability. As a result, a smaller grid size significantly increases the computation time, and cell size is therefore chosen so that computation time remains reasonable.

Another major limitation is the knowledge of depths. It is pointless to try to refine the resolution of a model if the environment is not described at an equivalent level. From this point of view, nautical charts cannot provide suitable bathymetric data for hydrodynamic modelling. because they are generated by soundings whose primary function is to identify elements affecting the safety of navigation. Information density is often sacrificed to enhance chart readability and the terrain that may pose a danger is highlighted, which can distort the objective representation of the seabed.

Validation with the hydrodynamic models developed by SHOM

Presentation

Since 2009, SHOM has developed five three-dimensional models (at different spatial scales) in the English Channel and Atlantic to meet new needs. These numerical models were developed using TELEMAC-2D and TELEMAC-3D code developed by the Laboratoire d'Hydraulique et d'Environnement (EDF).

The models describe the tidal currents in a marine area with relatively fine spatial resolution (100 km at sea, a few tens of meters near the coast).

Validation

The models are validated by comparing the simulation results with water depths predicted from sea level observations.

To qualify the models, comparisons are made between:

water levels by calculating the differences in amplitude (for high tide) between water levels predicted at different measurement points and levels extrapolated from the model at these same points;

mean phase differences in time between theoretical phases of high tide and low tide and observed phases of high tide and low tide.

The table summarizes the results obtained for the 3D models and illustrates the advantages compared to previous 2D models.

Model

Validation point

Amplitude deviation (cm)

Standard deviation (cm)

Low tide phase difference (minutes)

σ = standard deviation

High tide phase difference (minutes)

σ = standard deviation

Brest Roadstead 3D

13

4.7

2.4

9(σ=6)

3(σ=2)

English Channel 2D (1999)

172

15.3

12.3

13(σ=13)

11(σ=10)

English Channel 3D

190

9.1

7.1

8(σ=12)

8(σ=7)

Seine Bay 3D

25

7.6

7.1

5(σ=3)

6(σ=4)

Somme - Pas de Calais Bay 3D

28

6.4

4.1

4(σ=3)

8(σ=6)

Iroise Sea 3D

39

3.6

3.1

5(σ=2)

5(σ=2)

Advantages of of 3D hydrodynamic models compared to 2D

Improvements to numerical models and the transition from 2D to 3D results in better predictions (better accuracy of results) due to: